The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

Solve the following inequality: $|x-1|+|x-2|+|x-3| \geq 6$

$A$ man wants to cut three lengths from a single piece of board of length $91 \, cm$. The second length is to be $3 \, cm$ longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest board if the third piece is to be at least $5 \, cm$ longer than the second?

The values of $x$ for which the inequality $\frac{8x^2+16x-51}{(2x-3)(x+4)} > 3$ holds,are

Find all pairs of consecutive odd positive integers,both of which are smaller than $10$,such that their sum is more than $11$.

$A$ solution is to be kept between $68\,^{\circ} F$ and $77\,^{\circ} F$. What is the range in temperature in degree Celsius $(C)$ if the Celsius/Fahrenheit $(F)$ conversion formula is given by $F = \frac{9}{5} C + 32$?